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SageMath
E = EllipticCurve("jv1")
E.isogeny_class()
Elliptic curves in class 177450jv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177450.p1 | 177450jv1 | \([1, 1, 0, -130900, 18130000]\) | \(7225996599037/20321280\) | \(697591440000000\) | \([2]\) | \(1474560\) | \(1.7203\) | \(\Gamma_0(N)\)-optimal |
| 177450.p2 | 177450jv2 | \([1, 1, 0, -78900, 32742000]\) | \(-1582388942077/12602368800\) | \(-432615691462500000\) | \([2]\) | \(2949120\) | \(2.0669\) |
Rank
sage: E.rank()
The elliptic curves in class 177450jv have rank \(2\).
Complex multiplication
The elliptic curves in class 177450jv do not have complex multiplication.Modular form 177450.2.a.jv
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
